Related papers: $RLL$-realization of two-parameter quantum affine …
We introduce the two-parameter quantum affine algebra $U_{r,s}(\widehat{gl}_n)$ via the RTT realization. The Drinfeld realization is given and the type A quantum affine algebra is proved to be a special subalgebra of our extended algebra.
We obtain the basic $R$-matrix of the two-parameter Quantum group $U=U_{r,s}\mathcal(\mathfrak{so}_{2n})$ via its weight representation theory and determine its $R$-matrix with spectral parameters for the two-parameter quantum affine…
In this article we establish explicit isomorphisms between three realizations of quantum twisted affine algebra $U_q(A_2^{(2)})$: the Drinfeld ("current") realization, the Chevalley realization and the so-called $RLL$ realization,…
We further define two-parameter quantum affine algebra $U_{r,s}(\widehat{\frak {sl}_n})$ $(n>2)$ after the work on the finite cases (see [BW1], [BGH1], [HS] & [BH]), which turns out to be a Drinfel'd double. Of importance for the quantum…
The two-parameter quantum vertex operator representation of level-one is explicitly constructed for $U_{r,s}(C^{(1)}_n)$ based on its two-parameter Drinfeld realization we give. This construction will degenerate to the one-parameter case…
In this paper, we extend the Reshetikhin-Semenov-Tian-Shansky formulation of quantum affine algebras to the two-parameter quantum affine superalgebra $U_{p, q}(\widehat{\mathfrak{gl}}(m|n))$ and obtain its Drinfeld realization. We also…
Using super RS construction method and Gauss decomposition, we obtain Drinfeld's currents realization of two-parameter quantum affine superalgebra $U_{p,q}\widehat{(gl(1|1))}$ and get co-product structure for these currents.
We use the isomorphisms between the $R$-matrix and Drinfeld presentations of the quantum affine algebras in types $B$, $C$ and $D$ produced in our previous work to describe finite-dimensional irreducible representations in the $R$-matrix…
In this paper, we give an RTT presentation of the twisted quantum affine algebra of type $A_{2n-1}^{(2)}$ and show that it is isomorphic to the Drinfeld new realization via the Gauss decomposition of the L-operators. This provides the first…
The connection between the R-matrix realization and Drinfeld's realization of the quantum loop algebra $U_q(D^{(2)}_n)$ is considered using the Gaussian decomposition approach proposed by J. Ding and I. B. Frenkel. Our main result is a…
We give the explicit formula of the universal $R$-matrix of a double parameter (or two-parameter, or multi-parameter) quantum affine algebra of type ${\mathrm{A}}_1^{(1)}$. For $N$ with $q_{00}q_{01}$ being a primitive $N$-th root of unity,…
By generalizing the Reshetikhin and Semenov-Tian-Shansky construction to supersymmetric cases, we obtain Drinfeld current realization for quantum affine superalgebra $U_q[gl(m|n)^{(1)}]$. We find a simple coproduct for the quantum current…
In this paper, we present the hidden symmetry behind the Faddeev-Reshetikhin-Takhtajan-Semenov-Tian-Shansky realization of quantum affine superalgebras $U_q(\hat {osp}(1,2))$ and add the q-Serre relation to the Drinfeld realization of…
We describe the realization of the super Reshetikhin-Semenov-Tian-Shansky (RS) algebra in quantum affine superalgebras, thus generalizing the approach of Frenkel-Reshetikhin to the supersymmetric (and twisted) case. The algebraic…
We construct a Fock space representation and the action of the two-parameter quantum algebra $U_{r,s}(\frak{gl}_{\infty})$ using extended Young diagrams. In particular, we obtain an integrable representation of the two-parameter quantum…
We consider $\rm R$-matrix realization of the quantum deformations of the loop algebras $\tilde{\mathfrak{g}}$ corresponding to non-exceptional affine Lie algebras of type $\hat{\mathfrak{g}}=A^{(1)}_{N-1}$, $B^{(1)}_n$, $C^{(1)}_n$,…
We show that the quantum affine algebra $U_{q}(A_{1}^{(1)})$ and the quantum affine superalgebra $U_{q}(C(2)^{(2)})$ admit a unified description. The difference between them consists in the phase factor which is equal to 1 for…
Using the previous obtained universal $R$-matrix for the quantized nontwisted affine Lie algebras $U_q(A_1^{(1)})$ and $U_q(A_2^{(1)})$, we determine the explicitly spectral-dependent universal $R$-matrix for the corresponding quantum Lie…
We present an integral formula for the universal R-matrix of quantum affine algebra with 'Drinfeld comultiplication'. We show that the properties of the universal R-matrix follow from the factorization properties of the cycles in proper…
In our preceding research, we introduced the Drinfeld presentation of the quantum affine superalgebra associated to the orthosymplectic Lie superalgebra $\mathfrak{osp}(2m+1|2n)$ for $m>0$. We provided the isomorphism between its…